Steady-state Navier-Stokes Equations Research Articles

A variational finite element model for large-eddy simulations of turbulent flows

The authors introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation {T h } h>0. The eddy viscosity is expressed in terms of the friction velocity in the boundary layer due to the wall, and is of a standard sub grid-model form outside the boundary layer. The mixing length scale is locally equal to the grid size. The computational domain is the channel without the linear sub-layer of the boundary layer. The no-slip boundary condition (or BC for short) is replaced by a Navier (BC) at the computational wall. Considering the steady state case, the authors show that the variational finite element model they have introduced, has a solution (v h , p h ) h>0 that converges to a solution of the steady state Navier-Stokes equation with Navier BC.

유선형 형상 개선을 통한 고성능 EMU 열차의 공기저항 저감 연구

고성능 EMU 열차의 형상 개선을 통한 공기저항 저감 효과를 알아보기 위하여 3차원정상 Navier-Stokes 방정식과 2방정식 난류 모델을 이용한 전산유체역학을 이용하여 수치해석을 수행하였다. 전산시뮬레이션에는 FLUENTTM ver.13과 Gambit 2.4.6이 사용되었으며, 기본 형상과 유선형으로 개선된 형상에 대하여 계산을 수행하였다. 또한, 터널 내 주행 시의 공기저항 특성을 살펴보기 위하여 개활지에서의 공기저항 계산도 수행하였으며, 차량 별 공기저항 기여도에 대한 분석도 수행되었다. 유선형으로 개선된 형상의 열차는 절편형 전두부와 돌출된 상부 및 하부구조를 가진 기본 형상 열차에 비하여 약 9.8%의 공기저항이 저감된 것을 확인하였으며, 공기저항 저감에 따른 주행저항의 저감은 시속 80km/h에서 약 4%에 이르는 것으로 나타났다. The effect of modifying the shape of a high-performance EMU train on the aerodynamic drag is studied here using Computational Fluid Dynamics(CFD) based on three dimensional Steady-state Navier-Stokes equation and two equation turbulence modeling. FLUENT 12 and Gambit 2.4.6 are employed for a numerical simulation of the aerodynamic drag of a streamlined-shape train as well as a proto type train. The characteristics of the aerodynamic drag of trains in tunnels are analyzed in a comparison with these characteristics in an open space. The contribution of the aerodynamic drag of each case is also investigated to establish principal pertaining to drag reduction for urban trains in tunnels. The aerodynamic drag of a streamlined train was reduced to 9.8% relative to a proto-type train with a blunt nose and a protruding roof facility and underbody shape: the running resistance is expected to be reduced by as much as 4% at a running speed of 80km/h.

Fast solvers for discretized Navier-Stokes problems using vector extrapolation

We discuss the design and implementation of a vector extrapolation method for computing numerical solutions of the steady-state Navier-Stokes equation system. We describe a proof of concept implementation of vector extrapolation, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package ( http://www.manchester.ac.uk/ifiss ).

A Numerical Study Laminar Forced Convection of Air for In-line Bundle of Cylinders Crossflow

In the present paper, the numerical analysis is two-dimensional steady state Navier-Stokes equations and the energy equation governing laminar incompressible flow are solved using the finite difference method (FDM) and the technique body fitted coordinates (BFC). The constant heat flux is imposed on the surface of the tubes as the thermal boundary condition. The arrangement is considered in-line tube-banks the transverse ratio (ST/D) and longitudinal pitch-to-diameter ratio (SL/D) of 1.25, 1.75 and 2.25 respectively are also considered. Reynolds numbers of 30, 125 and 200, and Prandtl number are taken as 0.71. The temperature contours, local Nusselt number distributions to the tube surface and mean Nusselt number were analyzed in this paper. It was found of that the strength of the heat transfer between the surface of tubes and the air flow increases with increasing Reynolds number and increasing pitch-to-diameter rate.

On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations

When the artificial compressibility method in conjunction with high-order upwind compact finite difference schemes is employed to discretize the steady-state incompressible Navier-Stokes equations, in each pseudo-time step we need to solve a structured system of linear equations approximately by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the special structure and concrete property of the linear system we construct a structured preconditioner for its coefficient matrix and estimate eigenvalue bounds of the correspondingly preconditioned matrix. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods.

A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations

Abstract The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.

Numerical analysis of gasification performance via finite-rate model in a cross-type two-stage gasifier

The gasification process of a pressurized, oxygen-blown, entrained-flow E-Gas like gasifier through numerical modeling is investigated by solving the 3-D, steady-state Navier–Stokes equations with the Eulerian–Lagrangian method. Eight chemical reactions are solved via the Finite-Rate/Eddy-Dissipation Model. The preliminary gasification process is successfully modeled and the global chemical reactions are proved to be strongly affected by the finite rates. The results of parametric study show that the increasing O2/Coal ratio results in a decrease of CO, but an increase of CO2 and exit temperature. With a modified water–gas-shift reaction rate, a more reasonable trend is obtained that as the coal slurry concentration decreases, the mass flow rate of H2, CO2, and H2O increase while that of CO decreases. As the amount of coal slurry mass flow in the first stage increases, the exit temperature and the mole fraction of H2 and CO2 increase, while that of CO decreases. However, different fuel distributions do not provide notable influence on gasification performance due to the large space inside the E-Gas gasifier allowing complete reaction. The overall results show that the present CFD model can adequately capture the gasification behavior and analyze gasification performance inside the gasifier.

Optimized boundary driven flows for dynamos in a sphere

We perform numerical optimization of the axisymmetric flows in a sphere to minimize the critical magnetic Reynolds number Rmcr required for dynamo onset. The optimization is done for the class of laminar incompressible flows of von Kármán type satisfying the steady-state Navier-Stokes equation. Such flows are determined by equatorially antisymmetric profiles of driving azimuthal (toroidal) velocity specified at the spherical boundary. The model is relevant to the Madison plasma dynamo experiment, whose spherical boundary is capable of differential driving of plasma in the azimuthal direction. We show that the dynamo onset in this system depends strongly on details of the driving velocity profile and the fluid Reynolds number Re. It is found that the overall lowest Rmcr≈200 is achieved at Re≈240 for the flow, which is hydrodynamically marginally stable. We also show that the optimized flows can sustain dynamos only in the range Rmcr<Rm<Rmcr2, where Rmcr2 is the second critical magnetic Reynolds number, above which the dynamo is quenched. Samples of the optimized flows and the corresponding dynamo fields are presented.

Simulations of the Kirkendall-Effect-Induced Deformation of Thermodynamically Ideal Binary Diffusion Couples with General Geometries

The Kirkendall effect stems from the imbalance of atomic diffusion fluxes in a crystalline solid. Vacancy generation and annihilation, which compensate for the unbalanced fluxes, result in deformation that is experimentally observed as the motion of fiducial markers in a diffusion couple that can be approximated as a one-dimensional system. In multiple dimensions, such deformation occurs along both the directions parallel to and normal to the primary diffusion direction. In this article, we present a model that couples unbalanced interdiffusion and the resulting plastic deformation. One- and two-dimensional simulations are conducted with the analytically calculated diffusion coefficients of a thermodynamically ideal random alloy; the result shows that the ratio of the diffusion fluxes of the atomic species equals the ratio of atomic hop frequencies, which leads to the final volume ratio also given approximately by the hop frequency ratio if the initial volume ratio is equal. Moreover, the result also demonstrates that the conventional interdiffusion model fails to describe the Kirkendall void growth dynamics. For numerical implementation, we reformulate the diffusion equation to the smoothed boundary form and solve it within the deforming body governed by steady-state Navier-Stokes equation. This work demonstrates that the presented method can be a useful tool for studying Kirkendall-effect-induced deformation.

Generation of an average flow by a pulsating stream near a curved free surface

The generation of an average flow near a curved free surface under the action of small-amplitude harmonic translational vibrations is studied. It is found that, in contrast to the case of a flat non-deformable free surface, an average flow is generated in the viscous boundary layer. This flow, propagating in the bulk fluid, can be described by the steady-state Navier-Stokes equations with effective boundary conditions for the shear stresses. It is shown that, in contrast to the flow generation near a solid surface, the flow generated near the free surface depends on the fluid viscosity and the curvature of the surface.

On Landau’s solutions of the Navier–Stokes equations

A special class of solutions of the n-dimensional steady-state Navier–Stokes equations is considered. Bibliography: 23 titles.

On the Navier problem for the stationary Navier–Stokes equations

The Navier problem is to find a solution of the steady-state Navier–Stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary. If Ω is exterior it is required that the velocity converges to an assigned constant vector u 0 at infinity. We prove that a solution exists in a bounded domain provided ‖ a ‖ L 2 ( ∂ Ω ) is less than a computable positive constant and is unique if ‖ a ‖ W 1 / 2 , 2 ( ∂ Ω ) + ‖ s ‖ L 2 ( ∂ Ω ) is suitably small. As far as exterior domains are concerned, we show that a solution exists if ‖ a ‖ L 2 ( ∂ Ω ) + ‖ a − u 0 ⋅ n ‖ L 2 ( ∂ Ω ) is small.

Static characteristics of new type externally pressurized spherical air bearings

In order to provide some theoretical guideline for the structure design of the new type externally pressurized spherical air bearings, the static characteristics and the factors affecting the static characteristics of the air bearings were analyzed. A finite volume method was adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations, and a modified SIMPLE algorithm for compressible fluid was applied to solve the discretized governing equations. The pressure field and velocity field of the air bearings were obtained, and the factors and rules affecting the static characteristics were analyzed. The results show that the pressure of near air intakes can reach above 80% of air supply pressure, and there is a pressure steep fall around the air intakes. When the film thickness is greater than 20 μm, the bearing capacity rapidly decreases as film thickness increases. As the air supply pressure increases from 0.2 to 0.6 MPa, the maximum static stiffness increases by more than three times. The calculation method proposed well fits the general principle, which can be extended to the characteristic analysis of other air bearings.

On the existence of vanishing at infinity symmetric solutions to the plane stationary exterior Navier–Stokes problem

We study a nonhomogeneous boundary-value problem for the steady-state Navier–Stokes equations in a two-dimensional exterior domain with two orthogonal symmetry axes. The existence of a solution which tends to zero uniformly at infinity is proved under suitable parity conditions on the data of the problem. The result is obtained for arbitrary values of the flux of the boundary datum.

On the maximum modulus theorem for the steady-state Navier–Stokes equations in Lipschitz bounded domains

We prove that the steady-state Navier–Stokes problem in a Lipschitz bounded three-dimensional domain has a solution which satisfies a maximum modulus estimate, provided the fluxes of the boundary datum through the boundary of any interior connected component are less then a computable positive constant.

On symmetric Leray solutions of the stationary Navier–Stokes equations

A classical result of Amick (Acta Math 161:71–130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier–Stokes equations in the plane is extended to Lipschitz domains. This results is compared with the famous Stokes paradox of linearized hydrodynamics and applied to a mixed problem of some interest in the applications.

Residual reduction algorithms for nonsymmetric saddle point problems

In this paper, we introduce and analyze Uzawa algorithms for non-symmetric saddle point systems. Convergence for the algorithms is established based on new spectral results about Schur complements. A new Uzawa type algorithm with optimal relaxation parameters at each new iteration is introduced and analyzed in a general framework. Numerical results supporting the efficiency of the algorithms are presented for finite element discretization of steady state Navier–Stokes equations.

On the asymptotic behavior ofD-solutions of the plane steady-state Navier–Stokes equations

We prove that all the derivatives of a D-solution (u, p) of the Navier-Stokes equations in a plane neighborhood of infinity Cc R0 decay more rapidly than |x| ∈-1/2 for every positive ∈. Moreover, we show that if the flux of u through the boundary of C R0 is zero, the second derivatives of p are summable over the complement of C R0 .

A robust implicit multigrid method for RANS equations with two-equation turbulence models

The design of a new, truly robust multigrid framework for the solution of steady-state Reynolds-Averaged Navier-Stokes (RANS) equations with two-equation turbulence models is presented. While the mean-flow equations and the turbulence model equations are advanced in time in a loosely-coupled manner, their multigrid cycling is strongly coupled (FC-MG). Thanks to the loosely-coupled approach, the unconditionally positive-convergent implicit time-integration scheme for two-equation turbulence models (UPC) is used. An improvement to the basic UPC scheme convergence characteristics is developed and its extension within the multigrid method is proposed. The resulting novel FC-MG-UPC algorithm is nearly free of artificial stabilizing techniques, leading to increased multigrid efficiency. To demonstrate the robustness of the proposed algorithm, it is applied to linear and non-linear two-equation turbulence models. Numerical experiments are conducted, simulating separated flow about the NACA4412 airfoil, transonic flow about the RAE2822 airfoil and internal flow through a plane asymmetric diffuser. Results obtained from numerical simulations demonstrate the strong consistency and case-independence of the method.

L p -Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces

In this paper we address the existence, the asymptotic behavior and stability in L p and L p, ∞, , for solutions to the steady state 3D Navier–Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier–Stokes equations in L p spaces, and we prove the stability of these solutions. Namely, we prove that such small steady state solutions attract time dependent solutions with large initial velocity driven by the same forcing. We also give non-existence results of stationary solutions in L p , for .